I'm in a similar situation. I picked a career that has a large amount of public facing interaction. I had a prof tell me I'd have a hard time getting hired, I've been bribed to resign (or get fired) and I'm having a bitch of a time getting hired. Getting an interview is not a problem, it's getting hired. If public administrations hire a stutterer in a public facing capacity, it can be seen as making the town look bad, so I'm looking almost exclusively at the private sector. I have started saying I have a disability, but I have no idea if this help or hurts or matters at all. Good Luck.